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# Merry and Michelle play a card game. In the beginning

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Senior Manager
Joined: 21 Oct 2013
Posts: 414
Merry and Michelle play a card game. In the beginning  [#permalink]

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06 Jun 2014, 13:41
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

73% (03:02) correct 27% (03:07) wrong based on 208 sessions

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Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54
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Merry and Michelle play a card game. In the beginning  [#permalink]

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06 Jun 2014, 23:53
4
We can use the plugging in method to solve this problem.

So straight away if we start plugging in option C = 36. We get the number of cards for merry as 45(after rounding off) and number of cards for Michelle as 27- The numbers are reflected after the 3rd game. This is not correct as Merry ends up having only 14 cards extra. In this case, it is more than 14. So Eliminate C, D and E.
Now we can try with B.
 Number of Cards Game Michelle Merry Initially 27 27 After game 1 18 36 After game 2 30 24 After game 3 20 34

Now Merry has 14 cards more than Michelle. This option gives us exactly what number of cards they had initially.

So the answer is B.
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Re: Merry and Michelle play a card game. In the beginning  [#permalink]

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07 Jun 2014, 09:17
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Anyone solving this with equations?
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Joined: 13 Jun 2013
Posts: 270
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

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07 Jun 2014, 09:51
2
1
ronr34 wrote:
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Anyone solving this with equations?

no. of cards after each round are shown in the following figure.

after round 3, merry have 14 more cards than michelle.
i.e. (34x/27)-(20x/27)=14

14x/27=14; x=27 hence B
Attachments

1.PNG [ 4.95 KiB | Viewed 3307 times ]

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Posts: 56370
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

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07 Jun 2014, 10:19
2
ronr34 wrote:
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Anyone solving this with equations?

This question is a perfect candidate for plugging in the answer choices. Algebraic approach would be a waste of time.
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Posts: 160
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

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17 Sep 2016, 14:16
My 2 cents:
This question can also be solved logically. We need a number which can be divided by 3, three times. Hence it MUST be a multiple of 27. Here 27 and 54 satisfy this condition. We can start with 27 and solve as Gnpth has done. Solving one will tell us which one is the answer.
Cheers!!!
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Posts: 1329
Location: Malaysia
Re: Merry and Michelle play a card game. In the beginning  [#permalink]

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11 Feb 2017, 07:05
1
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Official solution from The Economist.

Numbers in the answer choices and a specific question ("...how many cards...") call for Plugging In The Answers. If you feel like writing down equations, or if you are stunned by a long convoluted story in the question, stop! These are stop signs for Reverse PI.

Assume the amount in the answer choice is the number of cards each players has in the beginning, and then follow the story in the problem. If everything fits - stop. Pick it. Otherwise - POE and move on, until you find an answer that works.

First, plug in answer choice C. Assume that each player had 36 cards in the beginning of the game. This is how the game proceeds:
Michelle      Mary
Equal amounts                                             36            36
Michelle gives 1/3 · 36=12 cards to Mary        24            48
Mary gives 1/3 · 48=16 cards to Michelle        40            32
Michelle gives 1/3 · 40 cards to Mary         40-40/3     32+40/3

The last turn cannot be accomplished because a third of 40 cards is not an integer number. POE C, and look for another answer choice.
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Re: Merry and Michelle play a card game. In the beginning  [#permalink]

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17 May 2017, 04:58
raghavsatwik to know which is better that totally depends on your strength in which you are comfortable
Personally for me plugging in is more easy and simple
while algebric is waste of time
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Merry and Michelle play a card game. In the beginning  [#permalink]

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11 Aug 2018, 00:40
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Start with value 3 for both the cases, and make a table as shown in the picture. When you arrive at a stage in which you can't further divide a number by 3, multiply all values by 3. The value you get at the top is the correct answer :27

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15339732912034606703989131863871.jpg [ 2.14 MiB | Viewed 913 times ]

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Everything is in flux, nothing stays still

MGMAT1 :590 Q42 V30 (07/07/18)
VERITAS :660 Q48 V33 (16/07/18)
GMATPREP1 :690 Q46 V36 (22/07/18)
GMATPREP2 :740 Q51 V39 (06/08/18)
ECONOMIST :740 Q49 V44 (11/08/18)
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PRINCETON :690 Q48 V38 (26/08/18)
MGMAT2 :720 Q43 V45 (02/09/18)
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Re: Merry and Michelle play a card game. In the beginning  [#permalink]

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18 Aug 2018, 20:11
1
goodyear2013 wrote:
Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18
B) 27
C) 36
D) 45
E) 54

Let x = the number of cards they each have at the beginning of the game.

After the first turn, i.e., after Michelle gives one-third of her cards (i.e., (1/3)x cards) to Merry, Michelle has x - (1/3)x = (2/3)x cards and Merry has x + (1/3)x = (4/3)x cards.

After the second turn, i.e., after Merry gives one-third of her cards (i.e., (1/3)(4/3)x = (4/9)x cards) to Michelle, Merry has (4/3)x - (4/9)x = (8/9)x cards and Michelle has (2/3)x + (4/9)x = (10/9)x cards.

After the third (or last) turn, i.e., after Michelle gives one-third of her cards (i.e., (1/3)(10/9)x = (10/27)x cards) to Merry, Michelle has (10/9)x - (10/27)x = (20/27)x cards and Merry has (8/9)x + (10/27)x = (34/27)x cards.

Since Merry ended up with 14 more cards than Michelle, we subtract the number of Michelle’s cards from the number of Merry’s cards, obtaining:

(34/27)x - (10/27)x = 14
(14/27)x = 14

x = 14 * (27/14)

x = 27

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Re: Merry and Michelle play a card game. In the beginning   [#permalink] 18 Aug 2018, 20:11
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